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Buchmann, Boris; Chan, Ngai Hang

Asymptotic theory of least squares estimators for nearly unstable processes under strong dependence. (English) Zbl 1126.62069

Ann. Stat. 35, No. 5, 2001-2017 (2007).
Summary: This paper considers the effect of least squares procedures for nearly unstable linear time series with strongly dependent innovations. Under a general framework and appropriate scaling, it is shown that ordinary least squares procedures converge to functionals of fractional Ornstein-Uhlenbeck processes. We use fractional integrated noise as an example to illustrate the important ideas. In this case, the functionals bear only formal analogy to those in the classical framework with uncorrelated innovations, with Wiener processes being replaced by fractional Brownian motions. It is also shown that limit theorems for the functionals involve nonstandard scaling and nonstandard limiting distributions. Results of this paper shed light on the asymptotic behavior of nearly unstable long-memory processes.

Cited in 2 Reviews
Cited in 23 Documents

MSC:

62M05 Markov processes: estimation; hidden Markov models
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62E20 Asymptotic distribution theory in statistics
62F12 Asymptotic properties of parametric estimators

Keywords:

autoregressive process; fractional noise; fractional integrated noise; fractional Brownian motion; fractional Ornstein-Uhlenbeck process; long-range dependence; nearly nonstationary processes; stochastic integrals; unit-root problem
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References:

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